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Theorem fr0 4863
Description: Any relation is well-founded on the empty set. (Contributed by NM, 17-Sep-1993.)
Assertion
Ref Expression
fr0

Proof of Theorem fr0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dffr2 4849 . 2
2 ss0 3816 . . . . 5
32a1d 25 . . . 4
43necon1ad 2673 . . 3
54imp 429 . 2
61, 5mpgbir 1622 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  =/=wne 2652  E.wrex 2808  {crab 2811  C_wss 3475   c0 3784   class class class wbr 4452  Frwfr 4840
This theorem is referenced by:  we0  4879  frsn  5075  frfi  7785  ifr0  31359
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-fr 4843
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